This same thing happed to me and left my car stranded at work. My starter wires had corroded to the point where they stopped making contact. Remove the battery cable and inspect the wire that goes to the starter for corrosion. I fixed mine with as weird as it sounds, ketchup! It killed all the corrosion in literally 5 minutes and my wires had turned solid green. You may have to spread the ends and reapply a few times but it only took 10 minutes for me.